6p+5t=-16 and 3p-3=3t

addition and substitution methods for solving linear equations

Solve the following system of equations for p and t using the addition method or the substitution method.

6p + 5t = -16

3p - 3 = 3t

Verify your answers by substituting the solutions for p and t into the original equations.

 May 09, 2014 solve for the unknown variables p and t by: Staff AnswerPart I 1st equation: 6p + 5t = -162nd equation: 3p - 3 = 3t Explanation:Solving for p and t using the addition elimination methodWe are going to multiply the 2nd equation by 2 and then subtract it from the 1st equation. Multiplying by 2 will change the first term in the 2nd equation to 6p, which is also the first term in the 1st equation. When we subtract the 2nd equation from the 1st equation, the variable p will be eliminated. This will leave us with an equation with only one variable (the variable t) to solve.Solution:Multiply the second equation by 23p - 3 = 3t2 * (3p - 3 = 3t)2 * (3p – 3) = 2 * 3tExpand the left side of the equation using the distributive law2 * (3p – 3) = 2 * 3t2 * 3p + 2 * (– 3) = 2 * 3t6p - 6 = 6t ----------------------------------------------------------------

 May 09, 2014 solve for the unknown variables p and t by: Staff ---------------------------------------------------------------- Part II Subtract 6t from each side of the equation 6p - 6 = 6t 6p - 6 - 6t = 6t - 6t 6p - 6t - 6 = 6t - 6t 6p - 6t - 6 = 0 Add 6 to each side of the equation 6p - 6t - 6 = 0 6p - 6t - 6 + 6 = 0 + 6 6p - 6t + 0 = 0 + 6 6p - 6t = 6 ----------------------------------------------------------------

 May 09, 2014 solve for the unknown variables p and t by: Staff ---------------------------------------------------------------- Part III The result obtained by multiplying the second equation by 2 is : 6p - 6t = 6 Subtract the result from the first equation 1st equation: 6p + 5t = -16 Result obtained by multiplying the second equation by 2: 6p - 6t = 6 6p + 5t = -16 - (6p - 6t = 6) ------------------- ? 6p + 5t = -16 - 6p + 6t = - 6 ------------------- 0 + 11t = -22 11t = -22 ----------------------------------------------------------------

 May 09, 2014 solve for the unknown variables p and t by: Staff ---------------------------------------------------------------- Part IV Divide each side of the equation by 11 11t = -22 11t / 11 = -22 / 11 t * (11 / 11) = -22 / 11 t * (1) = -2 t = -2 substitute -2 for the value of t in the first equation, and then solve for p 6p + 5t = -16 6p + 5 * (-2) = -16 6p - 10 = -16 Add 10 to each side of the equation 6p - 10 = -16 6p - 10 + 10 = -16 + 10 6p + 0 = -6 6p = -6 Divide each side of the equation by 6 6p = -6 6p / 6 = -6 / 6 p * (6 / 6) = -6 / 6 p * (1) = -1 p = -1 ----------------------------------------------------------------

 May 09, 2014 solve for the unknown variables p and t by: Staff ---------------------------------------------------------------- Part V the final answer is: p = -1 t = -2 ----------------------------------------------------------------

 May 09, 2014 solve for the unknown variables p and t by: Staff ---------------------------------------------------------------- Part VI ---------------------------------------------------- Verify your answers by substituting the solutions for p and t into the original equations. p = -1 t = -2 1st equation: 6p + 5t = - 16 6 * (-1) + 5 * (-2) = - 16 - 6 - 10 = - 16 - 16 = - 16, OK → p = -1 & t = -2 is a valid solution 2nd equation: 3p - 3 = 3t 3 * (-1) - 3 = 3 * (-2) - 3 - 3 = - 6 - 6 = - 6, OK → p = -1 & t = -2 is a valid solution Thanks for writing. Staff www.solving-math-problems.com